Average Error: 45.2 → 8.4
Time: 1.6s
Precision: 64
\[\mathsf{fma}\left(x, y, z\right) - \left(1 + \left(x \cdot y + z\right)\right)\]
↓
\[\left(\mathsf{fma}\left(x, y, z\right) - \left(x \cdot y + z\right)\right) - 1\]
\mathsf{fma}\left(x, y, z\right) - \left(1 + \left(x \cdot y + z\right)\right)
↓
\left(\mathsf{fma}\left(x, y, z\right) - \left(x \cdot y + z\right)\right) - 1
double code(double x, double y, double z) {
	return (fma(x, y, z) - (1.0 + ((x * y) + z)));
}
↓
double code(double x, double y, double z) {
	return ((fma(x, y, z) - ((x * y) + z)) - 1.0);
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original45.2
Target0
Herbie8.4
\[-1\]

Derivation

  1. Initial program 45.2

    \[\mathsf{fma}\left(x, y, z\right) - \left(1 + \left(x \cdot y + z\right)\right)\]
  2. Using strategy rm

  3. Applied +-commutative45.2

    \[\leadsto \mathsf{fma}\left(x, y, z\right) - \color{blue}{\left(\left(x \cdot y + z\right) + 1\right)}\]

  4. Applied associate--r+8.4

    \[\leadsto \color{blue}{\left(\mathsf{fma}\left(x, y, z\right) - \left(x \cdot y + z\right)\right) - 1}\]

  5. Final simplification8.4

    \[\leadsto \left(\mathsf{fma}\left(x, y, z\right) - \left(x \cdot y + z\right)\right) - 1\]

Reproduce

herbie shell --seed 2020078 
(FPCore (x y z)
  :name "simple fma test"
  :precision binary64

  :herbie-target
  -1

  (- (fma x y z) (+ 1 (+ (* x y) z))))